Ann took a taxi home from the airport. The taxi fare was $\$2.10$ per mile, and she gave the driver a tip of $\$5$. Ann paid a total of $\$49.10$. Write an equation to determine the distance in miles $(x)$ between the airport and Ann's home. Find the distance between the airport and Ann's home.
Explanation: Let $x$ be the distance (in miles) between the airport and Ann's home. The fare for ${x}$ miles at the rate of $\$2.10$ per mile is $2.1x$. Ann also gave the driver a $\$5$ tip. The total amount paid was $2.1x+5$. Since the total fare was $\$49.10$, let's set this equal to $49.1$ : $ 2.1x+5=49.1$ Now, let's solve the equation to find the distance between the airport and her home $(x)$. $\begin{aligned} 2.1x+5&=49.1\\ \\ 2.1x+5{-5}&=49.1{-5}&&{\text{subtract }5} \text{ from each side}\\ \\ 2.1x&=44.1\\ \\ \dfrac{2.1x}{{2.1}}&=\dfrac{44.1}{{2.1}}&&\text{divide each side by ${2.1}$}\\ \\ x&=21\end{aligned}$ The equation is $2.1x+5=49.1$. The distance between the airport and Ann's home is $21$ miles.